Hi Joseph,
Re (1) : If you use the correct formula for calculating d', then it will
automatically correct for unequal numbers of old and new pictures.
Re (2): I think this is no problem for calculating the SDT statistics,
but rather for the interpretation of your results - does it make sense
to compare responses to old stimuli+TMS and responses to new stimuli
without TMS...?
There is one very serious issue with calculating d' for your data,
however. In case you collected binary responses ("Is the picture old or
new?"), then for calculating d' you will have to assume that the
internal distributions for "signal" and "noise" have identical standard
deviations (cf. Macmillan & Creelman, 2005). It is known for a long time
that this assumption is frequently incorrect for experimental data
(e.g., Swets, 1986). And thus d' is not a valid measure of sensitivity
because it is strongly influenced by response bias (Verde, MacMillan, &
Rotello, 2006).
The simple solution (at least for future experiments) is to obtain
rating responses rather than binary responses - with these responses,
you can caculate for example the area under the ROC curve, which is a
valid index of sensitivity even if the SDs of the internal distributions
are unequal (Swets, 1986). Again, Macmillan & Creelman (2005) explain
in detail how to conduct such an experiment.
Macmillan, N. A., & Creelman, C. D. (2005). Detection theory: A user's
guide (2. ed.). Mahwah, NJ [et al.]: Lawrence Erlbaum Associates.
Swets, J. A. (1986). Indices of discrimination or diagnostic accuracy:
their ROCs and implied models. Psychological Bulletin, 99(1), 100-117.
Verde, M. F., MacMillan, N. A., & Rotello, C. M. (2006). Measures of
sensitivity based on a single hit rate and false alarm rate: The
accuracy, precision, and robustness of d ', A(z), and A '. Perception
and Psychophysics, 68(4), 643-654.
Best,
Daniel
--
Dr. Daniel Oberfeld-Twistel
Johannes Gutenberg - Universitaet Mainz
Department of Psychology
Experimental Psychology
Wallstrasse 3
55122 Mainz
Germany
Phone ++49 (0) 6131 39 39274
Fax ++49 (0) 6131 39 39268
http://www.staff.uni-mainz.de/oberfeld/